Mri tractography based transit time determination for nerve fibers

ABSTRACT

Magnetic resonance methods comprise tractographically establishing a path along a structure in a specimen and finding a distribution of structure radii or cross-sectional areas along the path. Based on the distribution and the path, end-to-end functional characteristics of the structure are estimated. For example, nerve transit times or distributions of transit times can be estimated for a plurality of nervous system locations such as Brodmann areas. Comparison of estimated transit times or distributions thereof between reference values or other values from the same structure can be used to assess specimen health.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a continuation of U.S. patent application Ser. No. 14/345,219,deposited Jun. 16, 2014, which is the U.S. National Stage ofInternational Application No. PCT/US2012/055458, filed Sep. 14, 2012,which was published in English under PCT Article 21(2), which in turnclaims the benefit of U.S. Provisional Application No. 61/535,851, filedSep. 16, 2011. The prior applications are hereby incorporated byreference.

STATEMENT OF GOVERNMENT RIGHTS

This invention was made with government support under a contract awardedby the Department of Health and Human Services, National Institutes ofHealth. The government has certain rights in the invention.

TECHNICAL FIELD

The invention pertains to magnetic resonance methods and apparatus forestimating nerve signal transit time distributions.

BACKGROUND

Magnetic resonance imaging (MRI) has been used with a variety ofspecimens in clinical and other applications. In many examples, imagesare based on differences in the so-called T₁ and T₂ relaxation times inthe specimen being imaged. In other examples, translational diffusioncan be used as a relaxation mechanism that produces image contrast.While in some specimens, translational diffusion of spins is isotropic,in many important applications, specimens exhibit structural featuresthat make isotropic translational diffusion unlikely. To evaluatediffusion anisotropies of a specimen, so-called diffusion tensor (DT)methods such as those described in Basser et al., U.S. Pat. No.5,539,310, can be used. These methods typically involve the applicationof pulsed-gradient magnetic fields in several directions. By evaluatingdiffusion anisotropies resulting from restricted or hindered diffusion,structural anisotropies can be identified and imaged as desired.

A variety of specimen parameters can be obtained using DT methods. Forexample, evaluation of water diffusion in brain white matter can provideestimates of the trace of the diffusion tensor, an apparent diffusioncoefficient, relative anisotropy, or a fractional anisotropy. Parameterssuch as these can be used to assess brain white matter, and similarproperties can be estimated for other specimens.

One application of DT based structural determination is DT-tractographythat permits evaluation of the orientation of anisotropic structuresthroughout a specimen. Some DT-based tractographic methods are describedin, for example, Burrus et al., U.S. Pat. No. 7,881,878, and Mori andvan Zijil, “Fiber tractography: principles and strategies—a technicalreview,” NMR Biomed. 15:468-480 (2002), both of which are incorporatedherein by reference. One important application of DT tractography is thetracking of nerve fibers although the orientation of other elongated orotherwise anisotropic structures in biological and non-biologicalsamples can be similarly investigated. While these tractography-basedspecimen evaluations can provide helpful structural information, theyoften do not provide information that is otherwise targeted to specimenproperties of interest.

SUMMARY

According to representative methods, a path along a specimen structureis established based on a direction of a diffusion tensor principal axisat a plurality of locations along the path. A geometrical characteristicof the specimen structure is estimated along the established path at aplurality of path locations based on identification of a restricteddiffusion direction, and contributions to a specimen function for theplurality of path locations are estimated based on the geometricalcharacteristic. A specimen functional value is estimated based on thecontributions. In some examples, the specimen structure is a nerve fiberbundle, and the specimen functional value is a nerve signal transit timeor a nerve signal transit time distribution associated with nerve signalpropagation in the fiber bundle. In some examples, the estimatedgeometrical characteristic is a cross-sectional area associated with oneor more fibers of the nerve fiber bundle, or a linear dimensionassociated with a fiber cross-section such as a diameter or an effectivediameter of the fiber cross section, wherein the effective diameter isdefined as a length corresponding to a diameter of a circle having anarea that is substantially the same as the cross-sectional area. In someexamples, the geometrical characteristic of the specimen structure alongthe established path is estimated based on a set of translationaldiffusion-weighted magnetic resonance signals associated with aplurality of diffusion-weighted field strengths and a plurality ofdiffusion-weighted field directions. In further examples, a signalportion in the set of signals is identified as corresponding torestricted diffusion, and a length associated with restricted diffusionis identified. In some examples, the set of field strengths isassociated with a plurality of b-values of applied pulse fieldgradients. In representative examples, the specimen characteristic is atransit time, a transit time distribution, an electrical resistance, ora flow resistance along the path, and the cross-section is determinedbased on at least one of hindered or restricted diffusion in thespecimen at a plurality of path increments. In typical examples, thecross-section is determined based on at least one of hindered orrestricted diffusion in the specimen at a plurality of path increments.In representative examples, the specimen is nerve or muscle tissue, andthe path is associated with a fiber or a bundle of fibers in the tissue.In one example, the path corresponds to a nerve fiber or fiber bundle,and the specimen function is a nerve signal transit time estimated asproportional to fiber diameter.

According to representative methods, a set of translationaldiffusion-weighted magnetic resonance signals associated with aplurality of diffusion-weighted field strengths and a plurality ofdiffusion-weighted field directions is obtained for a sample. A path anda cross-section along the path associated with at least one restrictedcompartment of the sample is established using the set of signals.

A specimen functional characteristic associated with the path and thecross section is estimated. In some examples, the set of signals is aset of image signals, and the path corresponds to an orientation of therestricted compartment. In other examples, a principal axis of adiffusion tensor is determined, and the path is selected based on theprincipal axis. In alternative examples, paths and cross-sectionsassociated with two or more restricted compartments, two or morehindered compartments are determined from the set of signals, andrespective functional characteristics are estimated. According torepresentative embodiments, the cross-section is a radius, diameter,length, width, cross-sectional area, or other value associated with sizeof the restricted compartment. In typical examples, signal portions ofthe set of signals corresponding to diffusion in the restrictedcompartment are associated with diffusion in an intra-axonal volume ofthe sample. In alternative examples, an estimate of a spin fractionassociated with restricted translational diffusion associated with anerve fiber is estimated.

Representative apparatus comprise a magnetic resonance imaging systemconfigured to obtain and record a set of translationaldiffusion-weighted magnetic resonance signals associated with aplurality of diffusion-weighted field strengths and a plurality ofdiffusion-weighted field directions in a specimen, and a processorconfigured to estimate a path of a structure in the specimen and across-sectional parameter of the structure at a plurality of pathlocations based on restricted diffusion associated with the specimen,and determine a functional characteristic of the structure based on thepath and the plurality of cross-sectional parameters. In some examples,a display is coupled to the processor and configured to display an imagecorresponding to the path and the specimen structure. In furtherexamples, the display is further configured to display path increments.In some examples, the processor is configured to estimate the path basedon at least one principal diffusion axis associated with the restrictedcompartment. In representative embodiments, the path is associated witha nerve fiber, a nerve fiber bundle, a muscle fiber, or a bundle ofmuscle fibers.

Methods of in vivo nervous system assessment include identifying nervepathways between a plurality of nervous system locations, andestablishing transit time moments between at least some of the nervoussystem locations based on the identified nerve paths and a distributionof nerve fiber radii along the paths. In some examples, the plurality ofnervous system locations includes a plurality of Brodmann areas. Inadditional examples transit time moments between a plurality oflocations are compared, and an assessment is provided based on thecomparison.

These and other features of the disclosed technology are set forth belowwith reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a representative method ofestimating nerve transit times based on axon paths and nerve fibercross-sectional diameters.

FIG. 2 is a block diagram illustrating a representative method ofassessing a specimen based on estimated axon transit times.

FIG. 3 is a block diagram illustrating a representative method ofassessing a specimen based on estimated axon transit time distributions.

FIG. 4 is a schematic block diagram of a representative magneticresonance (MR) apparatus configured to apply MR pulses to a specimen,determine one or more principal diffusivities and principal axes, andestimate transit times in nerve fibers or fiber bundles.

FIG. 5 is a schematic block diagram illustrating a method for modelingmagnetic resonance (MR) signals and extracting model parametersassociated with hindered and/or restricted spin diffusion in anisotropicspecimens.

FIG. 6 is a schematic diagram of a representative computing environmentfor directing the acquisition and processing of MR data, and providingcomparisons based on reference values.

DETAILED DESCRIPTION

As used in this application and in the claims, the singular forms “a,”“an,” and “the” include the plural forms unless the context clearlydictates otherwise. Additionally, the term “includes” means “comprises.”Further, the term “coupled” does not exclude the presence ofintermediate elements between the coupled items.

The systems, apparatus, and methods described herein should not beconstrued as limiting in any way. Instead, the present disclosure isdirected toward all novel and non-obvious features and aspects of thevarious disclosed embodiments, alone and in various combinations andsub-combinations with one another. The disclosed systems, methods, andapparatus are not limited to any specific aspect or feature orcombinations thereof, nor do the disclosed systems, methods, andapparatus require that any one or more specific advantages be present orproblems be solved. Any theories of operation are to facilitateexplanation, but the disclosed systems, methods, and apparatus are notlimited to such theories of operation.

Although the operations of some of the disclosed methods are describedin a particular, sequential order for convenient presentation, it shouldbe understood that this manner of description encompasses rearrangement,unless a particular ordering is required by specific language set forthbelow. For example, operations described sequentially may in some casesbe rearranged or performed concurrently. Moreover, for the sake ofsimplicity, the attached figures may not show the various ways in whichthe disclosed systems, methods, and apparatus can be used in conjunctionwith other systems, methods, and apparatus. Additionally, thedescription sometimes uses terms like “produce” and “provide” todescribe the disclosed methods. These terms are high-level abstractionsof the actual operations that are performed. The actual operations thatcorrespond to these terms will vary depending on the particularimplementation and are readily discernible by one of ordinary skill inthe art.

While the disclosed methods and apparatus can be applied to a variety ofspecimens, particularly specimens that exhibit anisotropic diffusion,for convenient explanation, examples described herein are generallybased on measurements of nerve fibers, fiber bundles, brain whitematter, and related structures. These examples are of practicalimportance. For example, magnetic resonance (MR) images of specimensexhibiting anisotropic translational diffusion such as brain whitematter can be used in the diagnosis and therapy of a variety ofdisorders as well as the assessment of normal and abnormal braindevelopment, degeneration, and aging. In addition to the evaluation ofneural white matter (which can include multiple fiber orientations),other normal and pathologic tissues can be evaluated. Representativetissues include ischemic tissues and tissues associated with cerebraledema, cerebral hematoma, cerebral neoplasm, cerebral metastases.Tissues can be associated with neurodegenerative diseases such asstroke, multiple sclerosis, Alzheimer's disease, and Huntington'schorea. Evaluation of the efficacy of drugs and other treatments can bebased on such path-based functional estimations as described herein.Other applications include neonatal screening and drug screening, aswell as other clinical and industrial applications. In some examples,assessments of other fibrous tissues such as muscle can be obtained. Aselected portion or portions of a specimen can be evaluated using theseMR techniques, or a plurality of locations can be evaluated and anassociated image assembled. For convenience in the followingdescription, evaluation of one or a few specimen portions is described.These portions can correspond to volume elements (voxels) of an MRimage. In typical examples, the disclosed methods and apparatus aredirected to evaluation of in vivo specimens for diagnostic purposes, butother in vivo or in vitro specimens can be similarly evaluated ornon-biological specimens can be evaluated.

For example, neurodegeneration such the axon demyelination associatedwith multiple sclerosis can be identified. A cancer treatment can beevaluated based on diffusion changes produced in response to thetreatment. The efficacy of drugs and other treatments can be evaluatedbased on such structural evaluations. Identification and evaluation ofrestricted diffusion in anisotropic specimens can also be used inneonatal screening, drug screening, food processing, and other clinicaland industrial applications. In other examples, fiber connectivity,white-matter integrity, and fiber-tracking in the vicinity of brainlesions can be evaluated. The methods presented herein can generally beapplied to the evaluation and characterization of other anisotropicspecimens that exhibit hindered and restricted diffusion

MR images are generally based on detection of a magnitude, phase,orientation, or other property of spins of one or more sampleconstituents. In some examples, a spatially varying magnetic field suchas a pulsed-gradient magnetic field is applied to a specimen to producea spatial variation in spin angular frequency, which results in aspatial variation in the phase of these spins. Spin encodings that makeMR signals sensitive to net spin displacements are referred to as hereinas diffusion-weighted spins, and such encodings are referred to asdiffusion encodings. Typical pulse sequences for diffusion weighting arebased on pairs of diffusion sensitizing gradients such as those ofStejskal-Tanner encoding. Diffusion-weighted MR signals and images arebased on such diffusion-weighted spins produced by such pulse sequences.Diffusion-weighted MR signals can be obtained that are associated withisotropic or anisotropic translational diffusion. Such signals arereferred to herein as “diffusion-weighted signals” and images based onsuch signals are referred to as “diffusion-weighted images.Representative diffusion weighted imaging methods are described in, forexample, Basser, U.S. Pat. No. 5,539,310, which is incorporated hereinby reference.

As noted above, the disclosed examples are generally described withreference to brain white matter. Brain white is anisotropic and occupiesa substantial fraction of brain volume. Brain white matter is composedof ordered fascicles whose axons are surrounded by a complexextra-axonal environment containing astrocytes, glia, and extracellularmatrix. Axons (nerve fibers) are structurally anisotropic as a functionof position due to the extension of the axons along a local axis. Someaxons have associated myelin sheaths, but small-diameter axons aretypically not myelinated. The orientation of this local axis typicallyvaries throughout a specimen, but in other anisotropic specimens a localaxis or other anisotropy can be constant throughout the specimen. Whitematter can be locally anisotropic with respect to a local axonal axis,and MR signals obtained from white-matter specimens can reflect thisanisotropy. In some specimens, axons are not locally aligned withrespect to a single axis.

Diffusion-weighted (DW) MR signals can be associated with spin diffusionparallel to and perpendicular to a local axonal axis (or a distributionof local axes) in intra-axonal volumes and/or extra-axonal volumes.Diffusion of spin-labeled species such as water molecules can beassociated with so-called “hindered” diffusion in an extra-axonal space,and “restricted” diffusion in an intra-axonal space. “Hindered”diffusion typically refers to tortuous diffusion around diffusionbarriers but without confinement to a particular volume, and“restricted” diffusion typically refers to diffusion constrained to avolume defined by surrounding diffusion barriers. MR signals can includecontributions associated with restricted diffusion in the extra-axonalspace as well, and such contributions can be analyzed in addition to theMR signal contributions associated with intra-axonal restricteddiffusion. The evaluation of hindered and restricted compartments invarious specimens, including the estimation of compartment shapes anddimensions as well as distributions of such shapes and dimensions isdescribed in Basser et al., U.S. Pat. No. 7,643,863, which isincorporated herein by reference.

In diffusion tensor imaging (DTI), diffusion tensor values for some orall voxels of a specimen can be obtained, and the diffusion tensor canbe represented based on its eigenvalues (principal diffusioncoefficients) with respect to principal axes of diffusion. In this way,the diffusion tensor in some or all voxels can be represented as aspatially varying ellipsoid having axis lengths corresponding to theprincipal diffusivities and orientations associated with the principalaxes. In the evaluation of elongated structures such as fiber bundles, adirection of the longest axis of this ellipsoid is typically associatedwith an orientation of a fiber bundle. The directionality (i.e.,elongation) of the diffusion tensor ellipsoid can be characterized by afractional anisotropy FA which ranges from 0 (isotropic diffusion) to 1(diffusion along only a single axis). This and other ways ofcharacterizing directionality are described in, for example, Mukherjeeet al., “Diffusion Tensor MR Imaging and Fiber Tractography: TheoreticalUnderpinnings,” Am. J. Neuroradial. 29:632-641 (2008) and Wedeen et al.,U.S. Pat. No. 6,614,226, both of which are incorporated herein byreference.

MRI evaluation of anisotropic specimens based on modeling oftranslational diffusion of spins can be briefly described as follows.Spins in anisotropic specimens typically can be associated with either ahindered compartment in which spins diffuse in three dimensions withoutsubstantial impairment or to a restricted compartment in which spindiffusion is confined in at least one direction due to specimenstructure. An MR signal can be decomposed into signal portionsassociated with a hindered spin fraction and a signal portion associatedwith a restricted spin fraction. The signal portion associated with thehindered spin fraction typically exhibits Gaussian diffusion decay whilethe signal portion associated with the restricted spin fraction exhibitsnon-Gaussian decay. In the restricted compartment, diffusion along oneor more axes can be assumed to be uncorrelated so that diffusion alongthese axes can be modeled independently. In some examples, diffusion ina restricted compartment can be modeled along some directions ashindered diffusion and associated with a Gaussian diffusion decay. Forexample, for spins confined within a cylindrical volume, diffusion alonga cylinder axis can be modeled as hindered, while diffusionperpendicular to the cylinder axis is restricted and exhibitsnon-Gaussian diffusion decay. In some cases, the restricted compartmentscan be represented as an ensemble of different, similar, or identicaldimensions but with different orientations. This modeling framework canalso reflect exchange of spins between the restricted compartment andthe hindered compartment, and a variety of diffusion models can beselected for modeling of the compartments based on, for example, MRsignal-acquisition characteristics. This modeling framework can bereferred to as a “composite hindered and restricted model of diffusion”(CHARMED).

DTI can determine the diffusion ellipsoid (i.e., principal axes andprincipal diffusion coefficients) in each voxel of interest. Byassociating the principal diffusion coefficient and the associatedprincipal direction with fiber orientation, a fiber path through aspecimen can be followed from voxel to voxel. In some examples, otherspecimen images or other information can be used in conjunction with thediffusion ellipsoid data to aid in tracking fiber from voxel to voxel.Fiber tracking (i.e., tractography) can be based on a variety oftracking algorithms. For example, fiber trajectories can be based onprincipal axis directions tracked from voxel to voxel in threedimensions based on the diffusion tensor in a local neighborhood,starting at one or more “seed” voxels. Fiber direction is mapped byfollowing principal axis directions, and changes at voxel edges asprincipal axis directions change. In some examples, a local 3 voxel by 3voxel volume is used in tracking, but larger neighborhoods can be used.Directional changes at any voxel boundary can be limited so as toreflect more likely specimen structures as large, abrupt directionalchanges are generally not present in most biological samples. Inaddition, tracking can be limited to voxels having suitably large valuesof FA as tracking based on voxels exhibiting lower anisotropies can tendto be less accurate. A variety of more sophisticated tracking methodscan be used as well, including sub-voxel based tracking methods,probabilistic methods, and methods associated with selection of suitableseed voxels from which fiber tracking is to start. Representativemethods are described in, for example, Chung et al., “Principles andLimitations of Computational Algorithms in Clinical Diffusion Tensor MRTractography,” Am. J. Neuroradiol. 32:3-13 (2011). The methods andapparatus described herein are not limited to any particulartractography method, and a particular method can be selected asconvenient for any particular example.

Diffusion-based MR measurements can also be configured to providedimensional data associated with hindered or restricted compartments.For example, diffusion-sensitizing pulse sequences based on pulsedgradient fields generally produce MR signals that decrease as a functionof elapsed time between the gradients. However, spins that are confinedso as to exhibit restricted diffusion can diffuse only to a compartmentboundary so that signal decrease as a function of elapsed time is lessthat of spins that can diffuse freely. Thus, by evaluation of diffusionweighed MR signals as a function of time, size characteristics such aslengths, widths, diameters, and volumes of restricted and/or hinderedcompartments can be estimated as well as distributions of such sizecharacteristics can be estimated. Representative methods are describedin Basser et al., U.S. Pat. No. 7,643,863. DTI images are generallyobtained by applying suitable magnetic field pulses along at least 6non-collinear axes (typically, along as many as 30 non-collinear axes toincrease signal to noise ratio) at a b-value that can be selected basedon the specimen to be investigated, with typical values in a range offrom about 500 s/mm² to about 1200 s/mm². For rectangular gradientpulses, b=γ²G²δ²(Δ−δ/3), wherein γ is gyromagnetic ratio, G is magneticfield gradient magnitude, δ is gradient pulse duration, and Δ isgradient pulse temporal separation. In addition, an image is alsoacquired at a low b-value or a 0 b-value.

A representative method 100 of determining specimen properties based ontractographic measurements and size or size distribution estimations ofhindered or restricted compartments is shown in FIG. 1. At 102, a pathof one or more fibers, fiber bundles, or other structures in a specimenis estimated in one or more voxels. This path determination isconveniently provided based on voxel diffusion tensor estimates for aplurality of voxels that can be retrieved from a database 104 orcalculated from acquired DT data at 106, or a combination thereof. Thedatabase 104 can include estimates of diffusion tensor principal axesand principal diffusivities associated with a plurality of specimenlocations. In addition, the database 104 can include compartment sizeestimates associated with the diffusion tensor estimates as well asestimates of compartment size distributions. For example, a fiber bundlecan include a plurality of fibers that are substantially aligned andhave common principal axes, but also include fibers having adistribution of fiber diameters or cross-sectional areas. The database104 can be provided with all of this information for use in subsequentprocessing steps, or the associated data can be generated and storedseparately as needed.

A fiber or fiber bundle path can be associated with a path directionthat indicates a local fiber orientation. At 110, a series of planesperpendicular to such a fiber or fiber bundle orientation along thefiber path is selected. For simplicity, the series of planes can beuniformly spaced along the fiber path, or a non-uniform spacing can beused. For path locations at which fiber or fiber bundle properties suchas orientation, shape, or cross-section are rapidly varying, moreclosely spaced planes may be more useful. At 111, a fiber transit timevalue is initialized, and at 112 an initial path location is selected.For this path location, an associated cross-sectional dimensionalparameter such as effective radius, area, or other dimension isestimated at 114. The estimate can be based on stored values ofpreviously analyzed q-space MR data from a database such as the database104, or an additional signal acquisition 115 can be initiated toestablish compartment dimensions and a distribution of compartmentdimensions at the selected location. As mentioned above, fibertractography data and cross-sectional data can be extracted based onapplication of a series of MR pulse sequences followed by suitableanalysis of the detected signals.

MR signals associated with diffusion can be produced using a pulsedfield gradient (PFG) sequence that is typically used in so-calledq-space MRI, but other pulse sequences can be used. In q-space MRI, asample portion is situated in a static magnetic field, typically for aduration long enough to permit some or all spins of one or more speciesin the sample portion to align with the static magnetic field. Aradiofrequency (RF) pulse generator is configured to produce an RF pulse(a so-called π/2-pulse) so that specimen spins are rotated into a planeperpendicular to the static magnetic field. A gradient pulse describedby a gradient-pulse waveform G(t) associated with a magnetic fieldgradient G₀ having an effective pulse duration δ is applied to produce aspin rotation of q=(½π)γG₀δ, wherein γ is a gyromagnetic ratio and q isthe magnitude of q. In some examples, the duration δ is sufficientlyshort so that spin displacements during the application of thegradient-pulse waveform G(t) are small compared to spin displacementsthat occur during a diffusion time Δ after which spin diffusion ismeasured, and spin diffusion during the gradient-pulse duration δ can beneglected. The magnetic field produced by application of thegradient-pulse waveform G(t) is a function of spatial coordinates, andapplication of the gradient pulse produces a spatially tagged spindistribution. During the diffusion time Δ, the spin-labeled species move(by, for example, diffusion) and the spatially tagged spin distributionchanges. Another RF pulse (a so-called π-pulse) is applied followed by areapplication of the PFG. The combination of the π-pulse and the PFGtends to reverse the spatial tagging of spins, but does not reversechanges in the spatial spin distribution associated with diffusion orother spin displacements. Therefore, the MR signal obtained afterapplication of this sequence can be associated with spin diffusion orother spin displacements in the specimen. Many other pulse sequences canbe used, and other examples are described in, for example, P. Callaghan,Principles of Nuclear Magnetic Resonance Microscopy (Oxford UniversityPress, 1991). In some examples, described in, for example, R. Kimmich,NMR: Tomography, Diffusometry, Relaxometry (Springer Verlag 1997), adiffusion sequence or “diffusion filter” can be applied before theimaging sequence.

If translational spin diffusion produces a 3-dimensional Gaussiandisplacement distribution and Δ«Δ, then an MR signal produced using thePGF sequence can be expressed as:

|E(q)|=exp(−4π² q ^(T) DqΔ),

wherein D is a diffusion tensor, and q^(T) is the transpose of q, i.e.,q^(T) is a row vector corresponding to the column vector q. Byapplication of a series of gradient pulses in different directions,estimates of the values of the elements of the tensor D can be obtained.Depending on magnitudes of the pulse-gradient duration δ and thediffusion time Δ, an effective diffusion time Δ_(eff)=Δ−δ/3 can be usedin the above expression instead of the diffusion time Δ. A similarexpression can be obtained for MR signals in isotropic specimens. Insome examples, expressions for MR signals can be expressed in terms of aso-called “b-value,” wherein b is proportional to a product of (γG₀δ)²and the effective diffusion time.

Fiber functional properties associated with the selected path incrementcan be estimated at 118 by selecting a suitable value based on fibercross section or other compartment parameter at the selected location.For example, nerve signal propagation speed v in nerve fibers can beexpressed as a function of fiber cross-section diameter D, i.e, v=v(D),and a transit time associated with signal propagation at the selectedpath location can be estimated based on the cross section and theincremental path length ΔL. For example, for a selected path element, anincremental transit time contribution ΔL/v(D) is summed with valuesassociated with other path increments at 120. In some examples,cross-sectional planes are equally spaced and transit time contributionscan be summed with a common path length ΔL. However, for unevenly spacedplanes, transit times are based on fiber cross-sectional diameter aswell as a fiber length increment associated with the selected location,and contributions can be expression as ΔL_(i)/v(D_(i)), wherein ΔL_(i)is an incremental length of an i^(th) path element, and D_(i) is anassociated cross-sectional area. In addition to estimating transit timefor the incremental path at the selected location, a transit timedistribution based on a distribution of fiber cross-sections can besimilarly obtained. For example, a particular path location can beassociated with a distribution P(D) of fiber cross-section diameters,and a transit time distribution estimated based on the distribution andthe propagation speed for each cross-sectional area. A fiber bundletransfer function can be estimated based on a product of transferfunctions for the path increments, and the incremental transferfunctions estimated as Laplace or Fourier transforms of path incrementimpulse response. At 122, if additional path locations are to beconsidered, an additional path location is selected at 112, and processsteps are repeated. If consideration of the entire path (or a selectedportion of a path) is complete, a sum value or an associated transformis reported at 124.

Transit times associated with path increments can be estimated based onmeasured or predicted relationships between conduction velocity and pathincrement cross-sectional dimensions. For example, in myelinatedperipheral nerve fibers, conduction velocity has been shown to beproportional to fiber diameter when fiber diameter and internodal lengthare proportional to each other. At some small fiber diameters,internodal length may cease to be proportional to fiber diameter, andconduction velocity may be substantially less. For central nervoussystem fibers, the proportionality between diameter and intermodallength may extend to smaller diameters due to a different myelinationstructure. Transit time dependence of fiber diameter and internodalseparation is discussed in detail in Ritchie, “On the relation betweenfibre diameter and conduction velocity in myelinated nerve fibres,”Proc. R. Soc. Lond. B 217:29-35 (1982), which is incorporated herein byreference.

In the example of FIG. 1, transit times (or a transit time distribution)associated with varying cross-sectional areas or other structuralcharacteristics that vary along a fiber path are estimated. However, inother examples, other path varying properties of a fiber-like orfiber-bundle-like structures can be estimated. For example, flowcharacteristics such as fluid resistance can be estimated based on fibercross sectional area, total restricted or hindered volume, viscosity asa function of path length, or varying spin density along a path of afiber or fiber bundle. For laminar flow in tube, an incremental fluidresistance is proportional to a ratio of a product of incremental lengthand viscosity to a fourth power of tube radius. Thus, based on a pathdetermination and an estimation of restricted compartment radius (orother cross sectional parameters), a total fluid resistance can beobtained as sum of such increments. Thermal characteristics of suchstructures can be similarly obtained. Additional electricalcharacteristics of fibers or other elongated structures such asresistance, capacitance, mutual and self-inductance, and propagationdelay can be estimated based on conductivity, area, and other parametersthat vary along a path length. For example, a total electrical pathresistance can be estimated as a sum of a product of incremental pathlengths and path varying ratios of ρ/A, wherein ρ is resistivity and Ais cross-sectional area. Using tractographically obtained paths andpath-varying geometrical and compositional characteristics of aspecimen, specimen functional properties can be estimated, even thosefor which direct determination of a path is difficult or impossible.

The method of FIG. 1 is provided as a representative example. Typically,a functional characteristic and a distribution of such a functionalcharacteristic for a structure can be represented as an integral ofcontributions along a path. For example, for nerve fibers, propagationspeed V can be expressed as V=kR₀, wherein k is a constant and R₀ is aninner diameter of a myelinated axon. An axon radius distribution p(R)can then be expressed as a function of propagation speed V, p(V).Accordingly, mean speed can be estimated as:

V

=∫Vp(V)dV.

Thus, mean speed is proportional to mean radius,

V

=k

R₀

. Higher order moments can be similarly obtained as:

V ^(n)

=∫V ^(n) p*(V)dV=k

R ₀ ^(n)

.

A distribution of fiber transit times can be obtained from adistribution of transit speeds along a path:

${p(\tau)} = {{p( {L/V} )} = {{p( {L/{kR}_{0}} )} = {\frac{kR_{0}^{2}}{L}{{p( R_{0} )}.}}}}$

A mean transit time can be determined as

τ

=∫τp(τ)dτ

and higher order moments determined as

τ^(n)

=∫τ^(n) p(τ)dτ.

Thus, using a distribution of axon radii determined based on restricteddiffusion, an MRI-based path determination, and a proportionalityconstant k, mean and other moments of a transit time distribution can beestimated. The constant k may be difficult to estimate, and variousratios including moment ratios can be used for assessment so thatdependence of k is eliminated. In one example, a first moment of avelocity distribution can be scaled as:

$\frac{\langle V \rangle}{\sqrt{\langle ( {V - \langle V \rangle} )^{2} \rangle}}$

and explicit dependence on k is eliminated.

Estimated transit time distributions, mean transit time, and othermoments can be used to indicate nerve pathway performance for theassessment and evaluation of disease and disabilities of the centralnervous system and the peripheral nervous system. In some cases,multiple nerve pathways can be evaluated in this way to provide atransit time matrix for connected regions. In one example, inter-regiontransit times for one or more Brodmann areas can be determined based onevaluation of selected pathways between these areas. For example, meantransit times τ_(ij) between i^(th) and j^(th) Brodmann regions can bearranged as a transit time matrix. Similar transit time moment matricescan also be provided for higher order moments. Unconnected areas can berepresented by leaving a blank in such matrices.

Referring to FIG. 2, a method of specimen evaluation based on transittimes includes determining one or more transit times at 202. Transittimes can be obtained for various portions of a specimen or using avariety of measurement conditions. In addition, a total measurement timecan be obtained for a specific structure or portions thereof, andevaluation of a structure can be based on one or more portions. At 204,corresponding reference values are retrieved from a database 205. Thereference values or ranges thereof can be associated with a variety ofnormal or abnormal specimen conditions such as, for human tissuespecimens, a variety of tissue types, patient age, gender, and one ormore diseases along with a typical range of normal values. At 208, oneor more measured values are compared with reference vales. At 212, adetermination is made as to whether the measured values are withinnormal ranges, or within ranges associated with one or more abnormalspecimen conditions. At 216, a report that values are within normalranges is provided while at 214 variances from normal values arereported. In some examples, a particular range associated with aspecimen abnormality can be used for comparison, and based on thecomparison, a likelihood that the specimen has such an abnormality canbe reported.

FIG. 3 illustrates a method 300 similar to that of FIG. 2 but based onone or more transit time distributions associated with distributions ofhindered or restricted diffusion compartments in a specimen along one ormore paths. At 302, a transit time distribution is estimated based onstructure path and diameter along the path. At 304, reference values areextracted from a database 305, and compared with the extracted referencevalues at 308. The measured and reference values are compared at 312,and based on the comparison, the measured values are reported as withina normal range at 316 or reported as varying from a normal range at 314.

The methods of FIGS. 2-3 are based on comparisons of measured specimenvalues with one or more stored values obtained based on evaluation ofother specimen so as to establish standard and abnormal ranges. In otherexamples, transit times or transit time distributions can be estimatedas shown in FIG. 1, and compared with measured values. Such a comparisoncan aid in assessment as any discrepancy between the estimated andmeasured values can be indicative of an unexpected or unexplainedspecimen condition, or failure to establish a suitable specimenstructure path. Comparisons can also be with respect to previousestimates for a selected specimen or patient, so the efficacy of atreatment or progress of a disease can be tracked.

FIG. 4 is a schematic illustration of a representative apparatusconfigured to provide specimen functional characteristics such as fiberbundle transit times using MR-based specimen analysis. As shown in FIG.4, the MR apparatus includes a personal computer 401 or other computingdevice such as a laptop, workstation, or tablet computer configured toselect one or more MR pulse sequences for the acquisition of diffusiontensor based images. The computer 401 can provide a user interface forcontrolling data acquisition, analysis, and storage. A diffusion tensor(DT) sequence/analyzer 402 is coupled to the computer 401 and isconfigured to establish suitable pulse sequences including numbers ofpulse, pulse duration, pulse strength, and pulse orientations, includinggradient pulse orientations. The DT sequencer 402 is coupled to an RFgenerator 404 that can produce RF pulses that are coupled into specimenby an RF transmit coil 405. An RF receiver 406 is coupled to detectsignals from the specimen via an RF receive coil 407, and a gradientcontroller 408 is configured to apply gradient magnetic fields to thespecimen with a plurality of gradient coils 409. An axial magnetic fieldcontroller is coupled to one or more axial magnet coils 411. The DTsequencer 402 is configured to apply the selected fields in a suitablesequence and to process the received data to determine specimenproperties of interest. Typically pulsed-field gradients (“PFGs”) areapplied along a plurality of directions to obtain diffusion-weightedimages or MR signals. These MR signals can be processed with computerexecutable instrumentation in a dedicated processor, in the DT sequencer402, or at the computer 401. In some examples, computer executableinstructions for processing of acquired MR data to obtain transittimes/distributions are provided at 414.

A representative method 500 of acquiring diffusion-based MR data isillustrated in FIG. 5. In a step 502, MR signals E(q,Δ) are obtained forvariety of q-values and q-directions. Signals can be obtained by fixinga magnitude and duration of an applied pulsed-gradient magnetic field oreffective magnitude of other spin-encoding magnetic field (i.e., fixingq), and varying the direction in which the encoding field is applied.After signals associated with the various directions are obtained, theq-value is changed and another series of signals at the variousdirections is obtained. Alternatively, signals can be obtained by fixingthe direction of the applied encoding field and varying q. The directionof the encoding field can then be changed, and signals as a function ofq can be obtained. Other signal acquisition sequences can be used.

After obtaining the MR signal E(q,Δ) for a variety of encoding fielddirections, model parameters associated with hindered spin diffusion aredetermined in a step 504. Typical model parameters determined in thisstep can include principal diffusivities λ_(//), λ_(⊥) and anorientation of the local axonal axis and can be based on diffusiontensor methods. A signal model for restricted diffusion perpendicular tothe local axonal axis is selected in a step 506. Representative signalmodels include the expressions of Neumann and Callaghan described aboveand those described in P. van Gelderen et al., “Evaluation of restricteddiffusion in cylinders. Phosphocreatine in rabbit leg muscle,” J. Magn.Reson. B. 103:255-260 (1994). Model parameters associated with theselected model are obtained in step 508. Typical parameters includediffusion constants D_(//) and D_(⊥) for diffusion parallel andperpendicular to the local axonal axis and a cylinder radius. In a step510, relative fractions of spins that exhibit hindered and restricteddiffusion can be estimated. In a step 512, modeled signals can becomputed and displayed with respect to measured signals, or comparedwith one or more baseline or control values associated with normaltissues or diseased tissues.

The method 500 of FIG. 5 shows steps performed in a specific order, butthese steps can be performed in different orders, and model parametersfor restricted and hindered signal components can be estimated in acommon step or in a series of steps. Different models can be selectedfor other specimens, and the cylindrical model described herein is onlya representative example.

FIG. 6 and the following discussion are intended to provide a brief,general description of an exemplary computing environment in which thedisclosed technology may be implemented. Although not required, thedisclosed technology is described in the general context ofcomputer-executable instructions, such as program modules, beingexecuted by a personal computer (PC). Generally, program modules includeroutines, programs, objects, components, data structures, etc., thatperform particular tasks or implement particular abstract data types.Moreover, the disclosed technology may be implemented with othercomputer system configurations, including hand-held devices,multiprocessor systems, microprocessor-based or programmable consumerelectronics, network PCs, minicomputers, mainframe computers, and thelike. The disclosed technology may also be practiced in distributedcomputing environments where tasks are performed by remote processingdevices that are linked through a communications network. In adistributed computing environment, program modules may be located inboth local and remote memory storage devices. In some examples, some orall portions of computing systems used to extract specimen paths frommagnetic resonance diffusion tensor pulse sequences and to obtaininformation concerning hindered and restricted compartment dimensionscan be co-located with an MR imaging system. In other examples, hardwarecan be configured to implement computer executable instruction fortractographic path determinations, compartment geometry extraction, andestimation of transit times or other specimen function based on datasupplied from remote MR imaging systems.

With reference to FIG. 6, an exemplary system for implementing thedisclosed technology includes a general purpose computing device in theform of an exemplary conventional PC 600, including one or moreprocessing units 602, a system memory 604, and a system bus 606 thatcouples various system components including the system memory 604 to theone or more processing units 602. The system bus 606 may be any ofseveral types of bus structures including a memory bus or memorycontroller, a peripheral bus, and a local bus using any of a variety ofbus architectures. The exemplary system memory 604 includes read onlymemory (ROM) 608 and random access memory (RAM) 610. A basicinput/output system (BIOS) 612, containing the basic routines that helpwith the transfer of information between elements within the PC 600, isstored in ROM 608.

The exemplary PC 600 further includes one or more storage devices 630such as a hard disk drive for reading from and writing to a hard disk, amagnetic disk drive for reading from or writing to a removable magneticdisk, and an optical disk drive for reading from or writing to aremovable optical disk (such as a CD-ROM or other optical media). Suchstorage devices can be connected to the system bus 606 by a hard diskdrive interface, a magnetic disk drive interface, and an optical driveinterface, respectively. The drives and their associatedcomputer-readable media provide nonvolatile storage of computer-readableinstructions, data structures, program modules, and other data for thePC 600. Other types of computer-readable media which can store data thatis accessible by a PC, such as magnetic cassettes, flash memory cards,digital video disks, CDs, DVDs, RAMs, ROMs, and the like, may also beused in the exemplary operating environment.

A number of program modules may be stored in the storage devices 530including an operating system, one or more application programs, otherprogram modules, and program data. A user may enter commands andinformation into the PC 600 through one or more input devices 640 suchas a keyboard and a pointing device such as a mouse. Other input devicesmay include a digital camera, microphone, joystick, game pad, satellitedish, scanner, or the like. These and other input devices are oftenconnected to the one or more processing units 602 through a serial portinterface that is coupled to the system bus 606, but may be connected byother interfaces such as a parallel port, game port, or universal serialbus (USB). A monitor 646 or other type of display device is alsoconnected to the system bus 606 via an interface, such as a videoadapter. Other peripheral output devices, such as speakers and printers(not shown), may be included.

The PC 600 may operate in a networked environment using logicalconnections to one or more remote computers, such as a remote computer660. In some examples, one or more network or communication connections650 are included. The remote computer 660 may be another PC, a server, arouter, a network PC, or a peer device or other common network node, andtypically includes many or all of the elements described above relativeto the PC 600, although only a memory storage device 662 has beenillustrated in FIG. 6. The personal computer 600 and/or the remotecomputer 660 can be connected to a logical a local area network (LAN)and a wide area network (WAN). Such networking environments arecommonplace in offices, enterprise-wide computer networks, intranets,and the Internet.

When used in a LAN networking environment, the PC 600 is connected tothe LAN through a network interface. When used in a WAN networkingenvironment, the PC 600 typically includes a modem or other means forestablishing communications over the WAN, such as the Internet. In anetworked environment, program modules depicted relative to the personalcomputer 600, or portions thereof, may be stored in the remote memorystorage device or other locations on the LAN or WAN. The networkconnections shown are exemplary, and other means of establishing acommunications link between the computers may be used.

In the example of FIG. 6, computer-executable instructions forprocessing MR signals are stored in a memory device 664. Theseinstructions can be configured for path determinations via tractographycompartment geometry determinations, and application of functionrelationships such as the dependence of nerve fiber transit time onfiber cross-section. Such instructions can be provided at a remotelocation as well, and executed remotely, or retrieved for local use. Inaddition, functional relationships associated with diffusion compartmentgeometries can be stored at 665. One or more processors can be coupledto one or more displays to as to show a specimen path with or without aspecimen image, and functional contributions associated with one or morepath increments can be displayed. In some examples, the path is shownalongside or in overlap with a specimen image.

Having described and illustrated the principles of the describedtechnology with reference to the illustrated embodiments, it will berecognized that the illustrated embodiments can be modified inarrangement and detail without departing from such principles. Forinstance, elements of the illustrated embodiment shown in software maybe implemented in hardware and vice-versa. Also, the technologies fromany example can be combined with the technologies described in any oneor more of the other examples. In view of the many possible embodimentsto which the principles of the disclosure may be applied, it should berecognized that the illustrated embodiments are examples and should notbe taken as a limitation on the scope of the disclosure. For instance,various components of systems and tools described herein may be combinedin function and use. I therefore claim as the invention all subjectmatter that comes within the scope and spirit of the appended claims.Alternatives specifically addressed in these sections are merelyexemplary and do not constitute all possible alternatives to theembodiments described herein.

I claim:
 1. A method of in vivo nervous system assessment, comprising:identifying pathways between a plurality of nervous system locations;establishing transit time moments between at least some of the nervoussystem locations based on the identified pathways and a distribution ofnerve fiber radii along the pathways; and arranging the transit timemoments as a matrix of transit time moments.
 2. The method of claim 1,wherein the arranging the transit time moments as a matrix includesindicating unconnected specimen locations.
 3. The method of claim 1,wherein unconnected specimen locations are indicated with blanks in thematrix of transit time moments.
 4. The method of claim 1, wherein thetransit time moments are mean transit times.
 5. The method of claim 1,wherein the transit time moments are mean square transit times.
 6. Themethod of claim 1, wherein the transit time moments are moments of ordern, wherein n is an integer greater than
 2. 7. The method of claim 1,wherein the pathways and the distribution of nerve fiber radii along thepathways are determined based on directions of an axis of a specimenstructure and establishing the pathways along the specimen structurebased on the directions of the axis of the specimen structure at aplurality of locations.
 8. The method of claim 1, further comprising:calculating a geometrical characteristic of a nervous system structurealong the pathways at the plurality of nervous system locations, whereinthe geometrical characteristic is a cross-sectional area, an effectivecross-sectional area, a linear dimension, or an effective radiusassociated with the cross-sectional area; calculating contributions tothe transit time moments for the plurality of nervous system locationsbased on the geometrical characteristic; and combining the calculatedcontributions along the respective pathways to determine the transittime moments.
 9. The method of claim 8, wherein the pathways and thedistribution of nerve fiber radii are associated with a nerve fiber, anerve fiber bundle, an axon, an axon bundle, or brain white matter andthe transit time moments are mean transit times along the pathways andare determined as proportional to nerve fiber radii.
 10. The method ofclaim 1, further comprising: applying a plurality of magnetic resonance(MR) pulse sequences to a specimen and obtaining MR images based on thepulse sequences; obtaining directions of an axis of a specimen structurebased on the MR images; establishing the pathways based on thedirections of the axis of the specimen structure at a plurality oflocations; calculating a geometrical characteristic of the specimenstructure along the established pathways at the plurality of locations,wherein the geometrical characteristic is a cross-sectional area or alinear dimension associated with the cross-sectional area; calculatingcontributions to the transit time moments for the plurality of locationsbased on the geometrical characteristic; combining the calculatedcontributions along the respective pathways to determine the transittime moments; and establishing the transit time moments by combining thecalculated contributions along the respective pathways.
 11. The methodof claim 10, wherein the MR pulse sequences are diffusion-weighted pulsesequences and the MR images are based at least one of restricteddiffusion and hindered diffusion associated with the specimen structure.12. The method of claim 11, wherein the pathways are established basedon one or more principal diffusion axes associated with restricted orhindered diffusion.
 13. A magnetic resonance apparatus, comprising: aplurality of field coils coupled to expose a sample to a plurality ofdiffusion-weighted pulse sequences; a receiver coil situated to receivemagnetic resonance signals from a specimen responsive to the pluralityof diffusion-weighted pulse sequences; and a processor operable toestimate pathways between a plurality of nervous system locations in thespecimen and cross-sectional parameters at a plurality of pathwaylocations based on the magnetic resonance signals, determine transittime moments based on the pathways and the cross-sectional parameters,and arrange the transit time moments as a matrix.
 14. The magneticresonance apparatus of claim 13, wherein the arranging the transit timemoments as the matrix includes indicating unconnected specimenlocations.
 15. The magnetic resonance apparatus of claim 13, wherein thetransit time moments are mean transit times.
 16. The magnetic resonanceapparatus of claim 13, wherein the transit time moments are moments oforder n, wherein n is an integer greater than
 1. 17. The magneticresonance apparatus of claim 13, wherein the pathways and a distributionof cross-sectional parameters along the pathways are determined based ondirections of an axis of a specimen structure and establishing thepathways along the specimen structure based on the directions of theaxis of the specimen at a plurality of locations.
 18. The magneticresonance apparatus of claim 13, wherein the cross-sectional parametersare cross-sectional areas or a linear dimensions associated with thecross-sections and contributions to the transit time moments for theplurality of nervous system locations are calculated based on thecross-sectional areas or the linear dimensions associated with thecross-sections and the calculated contributions along the respectivepathways are combined to determine the transit time moments.
 19. Themagnetic resonance apparatus of claim 13, wherein contributions to thetransit time moments are calculated for the plurality of nervous systemlocations along the pathways based on the cross-sectional parameters andthe calculated contributions are combined along the respective pathwaysto determine the transit time moments.
 20. The magnetic resonanceapparatus of claim 13, wherein the pathways between a plurality ofnervous system locations in the specimen and the cross-sectionalparameters at a plurality of pathway locations are estimated based onleast one of restricted diffusion and hindered diffusion.
 21. Themagnetic resonance apparatus of claim 13, wherein the pathways areestablished based on one or more principal diffusion axes associatedwith restricted or hindered diffusion.